Multiply the following complex numbers: $({-5-i}) \cdot ({2-2i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-5-i}) \cdot ({2-2i}) = $ $ ({-5} \cdot {2}) + ({-5} \cdot {-2}i) + ({-1}i \cdot {2}) + ({-1}i \cdot {-2}i) $ Then simplify the terms: $ (-10) + (10i) + (-2i) + (2 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -10 + (10 - 2)i + 2i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -10 + (10 - 2)i - 2 $ The result is simplified: $ (-10 - 2) + (8i) = -12+8i $